m. esteves, g. nord
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DESCRIPTION
M. Esteves, G. Nord. PSEM_2D. A process-based soil erosion model at the plot scale. DYNAS Workshop Rocquencourt 6 th -8 th December 2004. Introduction. PRIM_2D P lot R unoff and I nfiltration M odel (1999) PSEM_2D P lot S oil E rosion M odel (2003) These models were designed - PowerPoint PPT PresentationTRANSCRIPT
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M. Esteves, G. NordPSEM_2DDYNAS Workshop
Rocquencourt 6th-8th December 2004A process-based soil erosion model at the plot scale
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IntroductionPRIM_2D Plot Runoff and Infiltration Model (1999)PSEM_2D Plot Soil Erosion Model (2003)These models were designedto dynamically couple hydrological and soil erosion processesto predict the spatial pattern of overland flow hydraulicsto predict the spatial pattern of soil erosionto be used in natural slopes conditionsto consider complex rainfall eventsThe models work on a rainfall event basisPRIM_2D has been validated (Esteves et al., 2000, J. Hyd.,228)PSEM_2D model is still under evaluation (Nord and esteves, WRR, submitted)
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ObjectivesThe main goals areto improve our understanding of local overland flow hydraulics to develop a better understanding of soil erosion processesto bring a better description of the spatial and temporal variability of soil erosion at the plot scale
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Description of PRIM_2D and PSEM_2D Applications of PRIM_2DValidation of the model by comparison with observed data Effect of the micro-topographyEffect of soil surface features pattern (crusted soils)Applications of PSEM_2D Evaluation of the model by comparison with experimental dataSome numerical examples to show the capabilities of the modelAs a conclusion: Future researchPresentation outline
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Model description
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The model has three major components Overland flow (OF) is generated as infiltration excess rainfall (hortonian) OF is routed using the depth averaged two dimensional unsteady flow equations on a finite difference grid Rainfall and OF hydraulics are used to compute soil erosion A single representative particle size (D50)Model description
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The infiltration algorithm is based on the Green and Ampt equation (1911)ZfModel description : Infiltration
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Model description : Overland flowFully dynamic two dimensional unsteady flow equations (Barr de Saint-Venant) Continuity equation:
Momentum equations:
x direction:
y direction:ggravitational acceleration (m.s-2)hflow depth (m)Rrainfall intensity (m s -1)Irate of infiltration (m s -1)Soxground slope (x direction)Soy ground slope (y direction)Sfx friction slope (x direction)Sfy friction slope (y direction)uflow velocity (x direction) (m s -1)vflow velocity (y direction) (m s -1)
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Model description : Flow resistanceFriction is approximated using the Darcy-Weisbach equation
The Darcy-Weisbach friction factor is constantFor small depth flows (< 0.1 mm) the velocities are calculated using a kinematic wave approximation
x direction:y direction:ggravitational acceleration (m.s-2)hflow depth (m)Sfx friction slope (x direction) Sfy friction slope (y direction)uflow velocity (x direction) (m s -1)vflow velocity (y direction) (m s -1)fDarcy-Weisbach friction factor
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Model description : soil erosionTransport by runoffDetachment and re-detachment by raindrop impactDepositionEntrainmentDetachment by runoffDfd < 0Dfd > 0Drd > 0Tc> qs
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Model description: Soil erosionA covering Layer of loose sediment (Hairsine and Rose, 1991) is conceptualized as the percentage of a grid cell covered by a deposited layer of depth the median particle diameter D50.
Therefore is calculated as:
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Model description: Soil erosionSediment mass conservation equation (Bennet,1974)
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Model description: Soil erosionSoil detachment by rainfall is a function of the rainfall intensity (Li, 1979)Damping effect of the water film at the soil surface a soil detachability coefficient by rainfall (kg m-2 mm-1)p an exponent set to 1.0 according to the results of Sharma et al. [1993]h water depth (m)ld loose sediment depth (m)zm the maximum penetration depth of raindrop splash (m)R rainfall intensity (m s-1)whereBefore sediment movement(kg m-2 s -1)
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Model description: Soil erosionSoil detachment by rainfalle function of the area of the covering layer (0-1)a soil detachability coefficient by rainfall (kg m-2 mm-1)ad soil re-detachability coefficient by rainfall (kg m-2 mm-1)p an exponent (1.0) h water depth (m)zm the maximum penetration depth of raindrop splash (m)R rainfall intensity (mm h-1)(kg m-2 s -1)(kg m-2 s -1)DetachmentRe-detachmentAfter sediment movement
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Model description: Soil erosionSoil detachment or deposition by runoff : a model proposed by Foster and Meyer [1972]
When qsTc, excessive sediment deposition
(kg m-2 s-1)Tc sediment transport capacity of the flow (kg m-1 s-1)qs sediment discharge per unit flow width in the flow direction (kg m-1 s-1)
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Model description: Soil erosionWhen Tc>qs (Dfd>0) net erosion occurs and the detachment and entrainment rates are given by:
(kg m-2 s -1)(kg m-2 s -1)DetachmentEntrainmenttf is the flow shear stress in the flow direction (Pa)tc is the critical shear stress of a spherical sediment particle [Yang, 1996] (Pa)tsoil the critical shear stress of the soil (Pa)Kr is the rill erodibility parameter (s m1)Tc sediment transport capacity of the flow (kg m-1 s-1)qs sediment discharge per unit flow width in the flow direction (kg m-1 s-1)
- Model description: Soil erosionWhen Tc
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Model description: Soil erosion Flow sediment transport capacity is based on the flow shear stress tf (Foster, 1982)
hcoefficient of efficiency of sediment transport (m0.5 s2 kg 0.5 ) tf flow shear stress acting on the soil particles (Pa)tc critical shear stress of sediment (Pa) kan exponent taken as 1.5 (Finkner et al.,1989)(kg m-1 s-1)
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Model description: Numerical methods Hydrological model and erosion model are treated independently since it is assumed that the flow dynamics are not affected by the suspended sedimentThe Saint Venant equations are solved using the MacCormack schemeThe mass balance equation for sediment is solved using a second-order centered explicit finite difference schemeFor numerical stability of the scheme and computational efficiency the time step is optimisedTopographic elevations are re-estimated at each time step if there is runoff
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Model descriptionFlow chart of PSEM_2DModel description: Numerical methods To avoid directional bias of the Mac Cormack scheme the order is reversed every time step (predictor-forward, corrector-backward then predictor-backward, corrector-forward).
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Model description: Initial and boundary conditionsBoundary conditionsIn the plot version the boundaries are 3 non porous walls and an open boundary (outlet)Dummy cells are added to model wall boundaryAt the outlet no condition is required because the flow is supercritical
Initial conditionAt the beginning of the simulationh(x,y,0) = 0 u(x,y,0) = 0 v(x,y,0) = 0c(x,y,0) = 0 We consider that rainsplash transportation outside the plot is balanced by sediment coming from the area surrounding the plot.
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Model description : Calibrated parametersTransport by runoffDetachment and re-detachment by raindrop impactDepositionEntrainmentDetachment by runoffDfd < 0Dfd > 0Drd > 0Tc> qstsoilKraadhhf,f
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The model needs information onSlopes and elevations (Digital Elevation Model) Map of soil surface features distributionInfiltration parameters (hf, initial WC,Kc,Ks)Map of DW friction factorSoil erosion parameters (h,Kr, tsoil, D50)Map of a and ad, (ad=10 a) Rainfall (time, intensities)Model description: Data
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The parameter identification is carried out in three stagesWe started with parameters estimation based on physical characteristics and published dataSome of soil erosion parameters are defined using data available in the literature (ds=0.047, tsoil is estimated using the WEPP soil database)Calibration is undertaken for hf (crusted soils) and/or f on one rainfall eventCalibration is undertaken for h,Kr, tsoil using the ranges of values found in the literature
Model description: Parameter identficationWEPP: Water Erosion Prediction Project (US Dept. Agr.)
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Applications of PRIM_2D
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Examples of application PRIM_2DTwo runoff plots located on the same hillslopeHomogeneous soil surface feature (ERO) one type of crust: erosionHeterogeneous surface feature (JAC) erosion crust and sandy aeolian micro mounds
Grid resolution 0.25 by 0.25 m Both plots have the same subsoil Initial soil water content were obtained from neutron probe measurements Verification runs
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Examples of application PRIM_2DHomogeneous soil surface feature (ERO)Heterogeneous surface feature (JAC)Runoff plots in Niger (West Africa)
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Examples of application PRIM_2DEROSandy moundsErosion crustsJAC
JAC
ERO
Soil properties
Soil texture
Loamy sand
Loamy sand
(s sat. W C (-)
0.296
0.296
hf (m)
1.3795
1.3795
Ks (m/s)
2.15 E-05
2.15 E-05
Surface properties
Erosion
Zc (m)
0.005
0.005
hf (m)
1.3795
1.3795
Ks (m/s)
1.70 E-08
1.70 E-08
f
0.25
0.25
Sandy mounds
Zc (m)
0.05
hf (m)
0.18
Ks (m/s)
1.90 E-06
f
0.70
JAC
ERO
Length (m)
20.0
14.25
Width (m)
5.0
5.0
Max slope (x)
0.19
0.12
Max slope (y)
0.17
0.21
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PRIM_2D ValidationAn exemple of validation run
recap
2D 251D 25
Temps4440.054179seconde
Pluie3983.744121litres
H_initial0litres
Infiltration1478.771162litres
Parcelle0.100769litres
Exutoire2631.109565litres
Bilan0.031688litres
Tcumulhneg0
Duree du calcul5301.2
2504.870.00
erodzdx.grdfichier de pentes selon x
erodzdy.grdfichier de pentes selon y
rugero25.grdfichier de rugosits
solero.grdfichier sol
27.001dure de la simulation en minutes
0.001DT initial en seconde
0.0001H_FILM (mtres)
0hauteur d'eau initiale uniformement repartie sur le terrain
0.05CN pour le calcul de la stabilit
1coefficient de Boussinesq
1nb de type de sol
2.15E-05conductivite hydraulique Ksol
1.70E-08conductivite hydraulique croute
0.005epaisseur de la croute
0.214delta theta du sol de l'equation de Green et Ampt
0.245delta theta de la croute de l'equation de Green et Ampt
1.3795psi de Green et Ampt interface
1.3795psi greene et AMPts sol
72pas de temps d'criture des cartes en secondes
1pas de temps d'ecriture des resultats en secondes
1Unite pour les debits (0 l/s, 1 mm/h)
1(0) Infiltrabilite=0.0, (1) Infiltrabilite= GA, X>1 Infiltrabilite=X mm/h
1SF max
&A
Page &P
observe
Observmm/hl/s2695.7204/09/1994 23:42:09Pluie en mm/h
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1110.0000.00033
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47.37
47.37
47.37
47.37
47.37
47.37
47.37
47.37
47.37
47.37
47.37
47.37
47.37
47.37
47.37
47.37
47.37
47.37
47.37
47.37
47.37
47.37
47.37
47.37
47.37
47.37
47.37
47.37
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
26.47
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
33.96
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
28.13
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
30.51
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
43.9
43.9
43.9
43.9
43.9
43.9
43.9
43.9
43.9
43.9
43.9
43.9
43.9
43.9
43.9
43.9
43.9
43.9
43.9
43.9
43.9
43.9
43.9
43.9
43.9
43.9
43.9
43.9
43.9
43.9
43.9
43.9
43.9
43.9
43.9
43.9
43.9
43.9
43.9
43.9
43.9
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
41.86
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
36
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
64.29
64.29
64.29
64.29
64.29
64.29
64.29
64.29
64.29
64.29
64.29
64.29
64.29
64.29
64.29
64.29
64.29
64.29
64.29
64.29
64.29
64.29
64.29
64.29
64.29
64.29
64.29
64.29
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
9.38
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
14.29
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
24.66
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
58.06
69.23
69.23
69.23
69.23
69.23
69.23
69.23
69.23
69.23
69.23
69.23
69.23
69.23
69.23
69.23
69.23
69.23
69.23
69.23
69.23
69.23
69.23
69.23
69.23
69.23
69.23
78.26
78.26
78.26
78.26
78.26
78.26
78.26
78.26
78.26
78.26
78.26
78.26
78.26
78.26
78.26
78.26
78.26
78.26
78.26
78.26
78.26
78.26
78.26
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
78.26
78.26
78.26
78.26
78.26
78.26
78.26
78.26
78.26
78.26
78.26
78.26
78.26
78.26
78.26
78.26
78.26
78.26
78.26
78.26
78.26
78.26
78.26
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
85.71
85.71
85.71
85.71
85.71
85.71
85.71
85.71
85.71
85.71
85.71
85.71
85.71
85.71
85.71
85.71
85.71
85.71
85.71
85.71
85.71
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
81.82
64.29
64.29
64.29
64.29
64.29
64.29
64.29
64.29
64.29
64.29
64.29
64.29
64.29
64.29
64.29
64.29
64.29
64.29
64.29
64.29
64.29
64.29
64.29
64.29
64.29
64.29
64.29
64.29
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
48.65
48.65
48.65
48.65
48.65
48.65
48.65
48.65
48.65
48.65
48.65
48.65
48.65
48.65
48.65
48.65
48.65
48.65
48.65
48.65
48.65
48.65
48.65
48.65
48.65
48.65
48.65
48.65
48.65
48.65
48.65
48.65
48.65
48.65
48.65
48.65
48.65
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
51.43
51.43
51.43
51.43
51.43
51.43
51.43
51.43
51.43
51.43
51.43
51.43
51.43
51.43
51.43
51.43
51.43
51.43
51.43
51.43
51.43
51.43
51.43
51.43
51.43
51.43
51.43
51.43
51.43
51.43
51.43
51.43
51.43
51.43
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
22.22
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
29.51
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
69.23
69.23
69.23
69.23
69.23
69.23
69.23
69.23
69.23
69.23
69.23
69.23
69.23
69.23
69.23
69.23
69.23
69.23
69.23
69.23
69.23
69.23
69.23
69.23
69.23
69.23
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
85.71
85.71
85.71
85.71
85.71
85.71
85.71
85.71
85.71
85.71
85.71
85.71
85.71
85.71
85.71
85.71
85.71
85.71
85.71
85.71
85.71
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
52.94
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
105.88
105.88
105.88
105.88
105.88
105.88
105.88
105.88
105.88
105.88
105.88
105.88
105.88
105.88
105.88
105.88
105.88
112.5
112.5
112.5
112.5
112.5
112.5
112.5
112.5
112.5
112.5
112.5
112.5
112.5
112.5
112.5
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
138.46
120
120
120
120
120
120
120
120
120
120
120
120
120
120
120
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
94.74
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
46.15
36.73
36.73
36.73
36.73
36.73
36.73
36.73
36.73
36.73
36.73
36.73
36.73
36.73
36.73
36.73
36.73
36.73
36.73
36.73
36.73
36.73
36.73
36.73
36.73
36.73
36.73
36.73
36.73
36.73
36.73
36.73
36.73
36.73
36.73
36.73
36.73
36.73
36.73
36.73
36.73
36.73
36.73
36.73
36.73
36.73
36.73
36.73
36.73
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
42.86
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
54.55
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
39.13
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
34.62
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
17.65
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.84
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
11.39
0
Rainfall
Observed
Calculated
Time (s)
Discharge and rainfall intensity (mm/h)
04 september 94
nash
TempsObservCalculDiff1Diff2Ef0.928Qmax Obs.123.46
000.00Somme1260508.12Qmax Cal.128.45
5500.021259.44094426440.00Somme218864.46Debut obs.117
1110.0033.731259.44094426441137.65Moyenne obs.35.49Debut cal.55
12115.2847.09408.32342320851011.97Moyenne cal.35.74Tmax obs.3621
12624.6652.80117.2207235887791.91Tmax cal.3611
13138.8455.5211.2595524011278.21
13638.0857.616.7357660575381.25Ret max1.38mm
14146.3357.69117.5980641639128.94Imax pluie138.46mm/h
14649.1660.16186.8535608989121.15
15154.6463.92366.733151289786.16
15654.9267.97377.633544134170.37
16160.2372.61612.271685067153.12
16665.8377.42920.3924484301134.48
17175.9482.421636.372093556341.95
17682.7286.252231.250586962312.44
18183.5689.962310.698189446341.04
18684.0394.452356.1737199504108.60
19183.6897.312322.8789632894185.76
19686.0098.832551.3424024866164.66
20186.1899.502569.890786564177.29
20685.1399.002464.7331022308192.30
21183.5197.252306.1075624665188.76
21678.9094.831884.2143231553253.82
22175.5592.201604.7304980624277.23
22673.7190.111460.6796577812268.92
23172.1287.401342.118576476233.46
24172.5683.531374.1018270045120.31
25171.9881.251331.648244441185.98
25673.3980.411436.596924895549.26
29167.1658.171003.128123652580.77
29657.5454.50486.47433107149.26
30145.0550.9691.477181124634.95Figure 5
30640.3947.7024.06027025353.33
31633.3441.794.60991095871.31
32130.6339.3023.595029049175.23
32623.7237.11138.4280825538179.12
33124.8535.12113.1068093358105.44
34123.1331.74152.71680697774.20
34622.3530.51172.737260112566.59
35117.9529.78307.6295313222139.89
35618.2429.26297.4863269876121.33
37619.9128.69242.702813326577.10
39123.4829.31144.165238119733.97
40623.9629.79132.840677326833.93
41124.5130.04120.596295092830.57
41623.1130.32153.202996268652.03
42125.7630.6594.597616936823.89
42626.9130.7273.585778964814.50
43128.9730.4742.49838663362.27
43628.6130.1547.3252300882.39
44129.2529.9038.95582363950.43
45131.8329.4313.38445845855.76
45634.6429.190.71666899829.67
46132.2228.8910.657377828911.10
46633.1928.535.297562401421.71
47128.0427.8055.46074935080.06
47627.9527.0656.87850074040.79
48123.9526.25133.10196043825.28
50122.3023.43174.01156569251.29
50621.6522.84191.6094867361.43
51620.7921.72216.01875288380.87
52620.9221.58212.15034874180.43
53123.4221.67145.71400187393.07
53620.2321.79232.72749596932.42
54122.7721.99161.8041334370.61
54619.8422.26244.92376861565.84
55623.8422.74135.57424823551.22
56621.9923.71182.23595990182.96
57623.5825.12141.84377653192.38
59125.0727.47108.60382837935.75
59631.6328.2414.913325874211.49
60134.2128.951.635855165327.69
62134.4731.041.043104480111.76
63631.5331.8215.63496129210.08
64130.571524716831.9824.17765903351.98
65133.511874219132.083.90745674992.05
65634.071817601432.132.00728092063.78
69634.61678615430.160.760064646619.85
71131.651767723528.9114.72130508737.50
72628.921373693325.9143.12850102069.07
73126.755579054524.5276.2657075714.99
73621.802427622123.32187.31139700372.29
74620.892434535920.92213.04813439750.00
76117.300272790418.02330.81535651710.52
76618.220609932817.10298.18358523851.25
77116.948061625716.25343.75167516880.49
78117.501507294114.62323.53561262958.31
78616.45623173113.93362.23115685796.38
79113.822377229313.35469.42533998390.23
80112.663255558512.28520.99648670860.15
81611.541560857511.19573.46082830170.12
82610.475043421510.57625.6781637540.01
83111.826180937110.29559.91021879952.37
86112.520685702810.31527.52522586124.88
88617.170685050112.22335.546118728424.49
89115.995441105612.56379.983361396911.77
90118.668760136113.35282.90711461828.25
90620.000942354613.57239.867632865341.31
91122.277571411413.61174.531356145875.14
92121.31167601813.84200.985259200555.81
92617.966743408114.01307.015564236915.62
93118.172445962614.13299.849295212816.30
95117.767878928714.04314.024062298313.93
96117.824382425213.91312.024689215.33
98116.743519419113.29351.378159178811.90
100614.960142207412.85421.41770330544.44
101115.685481391212.78392.16362621918.44
106116.852874262314.92347.29038630523.75
107119.212091687815.53264.924821126813.56
108122.069249870216.21180.079038941934.35
110123.443417851119.72145.08648573813.88
112124.585719566223.26118.87286759391.76
113125.936153733524.5691.24928735771.91
113629.778948383225.1032.600156064221.85
114631.712195143226.4214.261256446827.99
115136.814864565526.961.758969688997.20
117138.264381320528.027.7049451774104.96
117635.472754363328.080.000251179954.69
118132.745297262727.957.525726474622.99
119126.917794680727.4273.45875557760.25
120625.482490756326.53100.1222826211.10
123127.203474085824.9268.64336144475.23
124628.05397282824.2655.273726081714.36
125130.454113424323.9825.346085482841.95
125625.633950259423.6597.11418101843.94
126621.069794136122.94207.90204961213.49
131124.18900271322.03127.68096708314.66
133624.324497484724.20124.63725238770.02
134128.252632897125.2152.35926361059.27
136130.367870000330.7726.22190665230.16
137132.579645631533.548.46203308460.92
137640.117236009335.0421.42424335625.75
138644.301045316937.9377.659139247940.57
142641.074295447543.6131.19995990166.45
143142.688098430844.3851.83273417992.85
144645.119661874452.3792.757294668852.55
145151.015803761354.59241.093962881312.80
146157.142061916557.23468.87228221290.01
147156.894355024659.81458.20621891188.52
147662.627894509460.60736.54114258084.12
148661.637075517461.15683.74261398330.24
149158.303331203660.85520.51182212036.51
149660.304160539660.06615.81189504130.06
150161.34148974858.58668.37175220577.61
151158.329369824154.01521.700628228818.65
152151.222685258949.93247.56134391961.66
153146.382768053946.57118.68283179950.03
155145.372393718839.7497.689318591531.73
155639.169158428938.1513.54648812271.04
157635.876049199832.600.15011